# Berkeley Fluids Seminar

## University of California, Berkeley

### Bring your lunch and enjoy learning about fluids!

Wednesday, December 9, 2015

3110, Etcheverry Hall, 12:00-13:00

** Giulio Facchini ** (IRPHE Institut Phenomenes Hors Equilibre, Marseille, France)

**Lifetime of anticyclone in rotating stratified flows, application to meddies **

Meddies are large coherent anticyclones which form at Gibraltar Straits, where warm and salty water from the Mediterranean sea exits in the Atlantic Ocean. These vortical structures show a striking long lifetime of 2-3 years. The understanding of the fundamental mecha- nisms which allow Meddies to persist for such a long time, motivates our experimental, numerical and theoretical study. We look at the time evolution of an isolated vortex generated by injecting a small amount of fluid at the center of a rotating tank filled with salty water linearly stratified in density. In experiments, the fluid motion is investigated using PIV techniques, providing the velocity field in the plane orthogonal to the vorticity vector. Our two control parameters are the background Coriolis and buoyancy frequencies. We observe that vortices universally take an ellipsoidal shape de- fined by the geostrophic equilibrium, and slowly evolve in a quasi- steady self-similar way. They expand in the radial direction and slow down, but remain extremely coherent over several hundreds of back- ground rotations. Fluid equations can be simplified in the limit of small Rossby and Ekman numbers. At the first order in time, we ob- tain a diffusion like equation for the pressure, the density anomaly and the azimuthal velocity in the vortex. The behavior of the vortex de- pends on the ratio between the background Coriolis and buoyancy fre- quencies. When these two frequencies are equal, an exact self-similar solution is found, predicting a simple power law for the time evolution of the Rossby number and, surprisingly, a diffusion of the azimuthal velocity profile in the radial direction only, even when the aspect ratio of the vortex is small (i.e. pancake shape, like in real meddies). Our analytical solution is in good agreement with our experimental and numerical results.